In many cases Te can not be measured, either because
the nebula is too faint or it is so cool that the temeprature-sensitive
diagnostic lines (for example [O III]
4363) are too
weak. Thus, there is interest in having an abundance indicator that uses
the strong forbidden lines.

as an indicator of O/H in H II regions. They noted, based on a sample of
extragalactic H II regions, that the measured Te,
O/H, and R23
were all correlated. This works because of the relationship between O/H
and nebular cooling: the cooling in the ionized gas is dominated by emission
in IR fine-structure lines (primarily the [O III] 52µm
and 88µm
lines), so as O/H increases, the nebula becomes cooler. In response, the
optical forbidden lines, especially the [O III] lines, become weaker as
O/H increases (excitation goes down as T decreases).

The R23 vs. O/H relation is fairly well calibrated
empirically (based
on abundances using the direct method) for log O/H between -3.5 and -4.0
(Edmunds & Pagel
1984).
For higher O/H, the strong-line method
breaks down because few measurements of Te exist; only
two measurements have been
made for H II regions with roughly solar O/H
(Kinkel & Rosa 1994;
Castellanos et al. 2001).
In this regime, the relation has been calibrated using
photoionization models (which I'll discuss later) that may have systematic
errors. One other complication is that for log O/H < -3.8, the relation
between R23 and O/H reverses, such that
R23 decreases with
decreasing abundance. The relation thus becomes double-valued, and at the
turn-around region the uncertainties in O/H are much larger. This occurs
because at very low metallicities the IR fine-structure lines no longer
dominate the cooling because there are too few heavy elements. As a result
the forbidden lines more directly reflect the abundances in the gas.

This double-valued nature of R23 has led some to seek
other strong-line diagnostics. The ratio [O III]/[N II]
(Alloin et al. 1979;
Edmunds & Pagel 1984)
has been promoted to break the degeneracy in R23. This
ratio does appear to vary monotonically with O/H, although the observational
scatter generally is larger than for R23. More
recently, the emission line ratio

(2.5)

has been calibrated as an indicator of O/H by
Díaz &
Pérez-Montero (2000).
S23 has the advantage of varying monotically over the
range -4.3 < log O/H < -3.7 in which R23 becomes
ambiguous. S23
does become double-valued for O/H > -3.4. Where this relation breaks
down is uncertain at present because there are too few measurements. In
addition, the ratio
[N II]6583 /
H has been promoted as
another possible measure of O/H
(van Zee et al. 1998;
Denicoló, Terlevich
& Terlevich 2002).
[N II] / H varies
monotonically with O/H over the
entire range over which it is calibrated, but the scatter is quite large,
especially at low values of O/H in dwarf irregular galaxies. Note that
S23 and [N II] /
H are employed here as
measures of the oxygen
abundance, not sulfur or nitrogen and are calibrated by direct measurements
of O/H. Thus, non-solar abundance ratios are not a concern.

At the same time, there are several limitations.

None of these strong-line diagnostics is well calibrated for
log O/H > -3.5. At higher metallicities, the calibration is largely
derived from photoionization models.

The accuracy of each of these calibrations is quite limited. For
R23 the usual quoted uncertainty is ±0.2 dex,
which is roughly
the scatter; in the turnaround region, the uncertainty is significantly
larger. The accuracy of S23 is probably about the
same; although
there are few data points to pin down the scatter at the present time.
The scatter in [N II] /
H is significantly
larger, about ±0.3
dex; most of this scatter is real, not observational.

The strong-line abundance relations are subject to systematic
errors, because the forbidden-line strengths depend on the stellar
effective temperature and ionization parameter as well as abundances.
If a galaxy has a low star formation rate and only low-luminosity
H II regions with cooler O stars, the empirical calibration could give
a systematically different O/H than a galaxy with many of the most
massive O stars and luminous giant H II regions.